$\begin{array}{1 1}(a)\;500m\\(b)\; 600m\\(c)\;700m\\(d)\;800m\end{array}$

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Covering range $R\propto \sqrt h$

(ie) $R^2\propto h$

If range is to be tripled

$R'=3R$

$\big(\large\frac{R}{3R}\big)^2=\frac{h}{h'}$

$\large\frac{1}{9}=\frac{h}{h'}$

$h'=9h$

Height of the tower initially $h=100m$

$h'=9\times 100$

$\;\;\;\;=900m$

$\therefore$ The height of the tower has to be increased by

$h'-h=900-100$

$\Rightarrow 800m$

Hence (d) is the correct answer.

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